I have written
an essay on modern cosmology which is here. The essay touches on the significance of the cosmic
microwave background (CMB) anisotropy
and on other observational evidence for the Big Bang

If you read this essay you will have noticed this
intriguing statement:

‘In
fact the lack of power in the angular spectrum at very large scales, first seen
in COBE and confirmed in WMAP, (certainly at the quadrupole, l = 2,
and to some extent at the octopole) has been remarked on by a number of
observers (22). However for multipole l › 3, agreement with the
standard model is remarkable. (The Integrated Sachs-Wolfe effect predicts
enhanced power at low values of the multipole and WMAP and COBE data trend in
the opposite sense….’

This
is something of a puzzle, as
such a good match across the spectrum between theory and observations is
spoiled by unexplained data at large angular scales.

What
this means is that the minute ripples in the microwave background
(the 2.7° Kelvin radiation echo from the Big Bang) tell us a huge amount
about the early universe.The essay
explains some of this, but suffice to say that ripples occur at a wide range of
angular scales – there are very fine ripples and very broad ripples (we call it
‘scale-invariant’). The WMAP and COBE measurements have a puzzling lack of
‘rippliness’ on the biggest scales – ripples which cover dimensions of 60° to 90°
in the sky (which is the angular scale of the l = 2 quadrupole) or about
16 billion light years across on the surface of last scattering (the spherical
surface 13.7 billion light years away from which the microwave background that
is currently observed arose)

An intriguing paper in
Nature puts forward an
hypothesis for this loss of power at large angular scales (1) The hypothesis is that the universe is finite and closed and has the
spatial topology of a Poincaré spherical dodecahedron with opposite faces
abstractly glued together so that as you exit or look out of one face you enter
or look into the opposite face.

[A
spherical dodecahedron is to a Euclidean dodecahedron (like the one illustrated
above) as a spherical pentagon (12 of which when fitted together
form a sphere) is to a plane pentagon.In the same way as 12 spherical pentagons fit together perfectly to make
a sphere, which is the surface of a 3-D ball, 120 spherical dodecahedrons fit
together perfectly to make a hypersphere which is the 3-D surface of a 4-D
ball].

Because such a universe would be finite and closed it could
not sustain the largest scale ripples in the microwave background.The size of the biggest ripples would be
constrained by the finite size of the universe.This would explain the lack of power in the low multipoles of the
CMB.There are many possible finite
topologies for the universe – this dodecahedral one predicts the relative
'rippliness’ of the microwave background at the biggest scales of the dipole, the
quadrupole and the octopole (l=1, l=2 and l=3) very well.

This is only a hypothesis at the moment and it presents some
problems – inflation for example is well supported by other observations and
explains the homogeneity of the universe and the fact that it is flat or nearly
so – it is not clear whether an inflationary epoch can be supported in models
that result in a ‘small’ universe.

There are ways to test this hypothesis experimentally: first
it predicts Ω0 ≈ 1.013 >
1 (Ω0 = 1 for a flat, infinite universe).If Ω0 is found to be less than 1.01 the dodecahedral hypothesis is
disproven. (WMAP measures Ω0 = 1.02 but is insufficiently accurate to rule
out Ω0 < 1.01; and the
new satellite experiment, Planck, will give a more accurate measurement).Second, interconnected space topologies such
as this would produce correlations of temperature on matching circles in the
sky (3).None have been found in WMAP data
so far, but a very sensitive measurement would be required, to remove other
artefacts and noise.

It
will be interesting to see whether future data will support this
hypothesis.If it does, we might
find we live
in a universe that is finite and ‘only’ a few billion or tens of billions of
light years across.